Auc2Charge: An Online Auction Framework for Electric ... · Auc2Charge: An Online Auction Framework for Electric Vehicle Park-and-Charge Qiao Xiang1, Fanxin Kong1, Xue Liu1, Xi Chen1,

Auc2Charge: An Online Auction Framework forElectric Vehicle Park-and-Charge

Qiao Xiang1, Fanxin Kong1, Xue Liu1,Xi Chen1, Linghe Kong1 and Lei Rao2

1School of Computer Science, McGill University2General Motors Research Lab

July 16th, 2015

Qiao Xiang et al. (McGill) ACM e-Energy’15 07/16/2015 1/ 26

Introduction Electric Vehicles

Introduction

Electric Vehicles(EV)

Crucial component of Intelligent TransportationSystem(ITS)

Shift energy load from gasoline to electricity

Cause high penetration of power grid

Require large-scale deployment of charging stations

Various charging stations


Introduction Park-and-Charge

Park-and-Charge

An up-and-coming mode for charging stationsA parking lot equipped with Level 1 and Level 2 chargers

EVs get charged during parking, e.g., a few hours

Slow charging, inexpensive hardware and high utilizationof space

Parking Lot

Charging Points

A

B

C

A

B

C

Controller

Figure: An illustration of park-and-charge


Introduction Park-and-Charge

Current Field Deployment

Workplace, airport, military base and etc.Pricing policies

Pay-per-useFlat rate

Boston University Seattle-Tacoma Airport

Sources:bu.edu and plugincars.com


Motivation and Challenges Motivation

Pay-Per-Use and Flat-Rate Pricing

Advantages

Simple and straightforward

Helpful for early market expanding

Limitations

Overpricing and underpricing

Undermined social welfare i.e., sum of stationrevenue and user utilities



Social Welfare in Park-and-Charge: An Example

Pay-per-use and flat-rate: allocate 15kWh to each EV

A

B

A

B

SOC: 5/25

SOC: 20/40 SOC: 35/40

SOC: 20/25

+15

+15

Park and Charge

However,Marginal utilities of EVs are different

Lower arriving SOC → Higher marginal utility

Ignorance of such difference → Undermined social welfare



Social Welfare in Park-and-Charge: An Example

To maximize social welfare:

Allocate electricity to low SOC vehicle as much as possible

A

B

A

B

SOC: 5/25

SOC: 20/40 SOC: 30/40

SOC: 25/25

+10

+20

Park and Charge

Pay-per-use and flat-rate focus on station revenue, not socialwelfare.



Motivation

Future market deployment of park-and-chargedesires an efficient market mechanism to

Avoid overpricing and underpricing

Maximize social welfare


Motivation and Challenges Our Focus

Our Focus

Our Focus

Investigate auction as market mechanism forpark-and-charge

Auc2Charge: an online auction framework

Understanding system benefits via numericalsimulation


Motivation and Challenges Related Work

Related Work

Auctions has been widely studied in Internet Adwords,cloud computing and smart grid.

Social welfare maximizationTruthfulness and individual rationality

What enables Auc2Charge?

Budget-constrained online auction and randomizedauction theory

Auc2Charge can be extended to other operation modes ofcharging stations, e.g., fast charging reservation.


System Settings and Problem Formulation


3DUNLQJ�/RW

&KDUJLQJ�3RLQWV

$

%

&

$

%

&

&RQWUROOHU

Bid 1 2-‐3pm, $0.50, 5kWh Bid 2 3-‐4pm, $2.00, 9kWh

SOC: 60%

. . .

Win

Lose

EV Customer 1

Bid 1 2-‐3pm, $1.50, 6kWh Bid 2 3-‐4pm, $3.00, 8kWh

SOC: 30%

. . .

Win

Win

EV Customer N

. . . .

Bids Bids

AllocaK

on and

Pay De

cision

AllocaKon and

Pay Decision

EVs arrive, park-and-charge, and leave

Users send bids on how much to charge, when to charge andhow much to pay, i.e., {bkj (t), ckj (t)}, to the charging station

Auctions are conducted every time slot, and users get notified

Users can adjust future bids anytime during parking,



A Binary Programming Formulation

PNC : maximizeT∑t=1

M∑j=1

K∑k=1

bkj (t)y

kj (t) Social Welfare

subject toK∑

k=1

T∑t=1

bkj (t)y

kj (t) ≤ Bj , ∀j , Users Budget

M∑j=1

K∑k=1

ckj (t)ykj (t) ≤ R(t), ∀t, Station Supply

K∑k=1

y kj (t) ≤ 1, ∀j and t, No Double Wins

K∑k=1

ckj (t)ykj (t) ≤ Cj(t), ∀j and t, Unit-Time Charging Capacity

y kj (t) ∈ {0, 1}, ∀j , k and t. Winning Indication


System Settings and Problem Formulation Challenges

Challenges

PNC is NP-hard→ The auction must be computationallyefficient

PNC is stochastic→ The auction must be online

Users may bid strategically→ The autcion must be truthful and individualrational


Auc2Charge: An Online Auction Framework Auc2Charge in a Nutshell

Auc2Charge in a Nutshell

1. Decompose PNC into smaller auctions via bidsupdate process.

PNC

PNCone(1)

PNCone(2)

PNCone(t)

PNCone(T)

Bids Update Process




Bids Update Process:

Originally proposed in budget-constrained online Adwordsauction1, and extended to resource auction in cloudcomputing.2

Intuition: adjust reported valuation in PNCone(t) basedon the results from PNCone(t− 1)

Users not getting electricity in t − 1→ No adjust in t

Users getting electricity in t − 1→ Reduce reported valuation in t based on remaining budget

Rationale: avoid user depleting budget fast without fullycharged

Result: the overall budget constraint is dropped.1Buchbinder, Niv, et al. ”Online primal-dual algorithms for maximizing ad-auctions revenue.” Algorithms-ESA

2007.2Shi, Weijie, et al. ”An online auction framework for dynamic resource provisioning in cloud computing.”

ACM SIGMETRICS 2014.



A Binary Programming Model without Budget Constraint

PNCone(t) : maximize p(t) =M∑j=1

K∑k=1

ωkj (t)y

kj (t), Social Welfare

subject toM∑j=1

K∑k=1

ckj (t)ykj (t) ≤ R(t), Station Supply

K∑k=1

y kj (t) ≤ 1, ∀j No Double Wins

K∑k=1

ckj (t)ykj (t) ≤ Cj(t), ∀j Unit-Time Charging Capacity

y kj (t) ∈ {0, 1}, ∀j and k. Winning Indication




2. Execute randomized auction for PNCone(t)

PNC

PNCone(1)

PNCone(2)

PNCone(t)

PNCone(T)

Aucone

Aucone

Aucone

Aucone




Randomized Auction Aucone

Basic idea: design truthful mechanism via approximationalgorithm3

1 Perform a fractional VCG auction for PNCone(t)2 Decompose fractional solutions to PNCone(t) into a

polynomial number of feasible solutions3 Randomly select one feasible solution as the allocation

decision4 Compute the corresponding pricing decision

3Lavi, Ron, et al. ”Truthful and near-optimal mechanism design via linear programming.” Journal of the ACM

(JACM) 58.6 (2011): 25.




How to find a polynomial number of feasible solutions?

Use a greedy primal-dual approximation algorithm forPNCone(t) as a separation oracle

Greedy approximation algorithm

Drop bids exceeding the unit-charging capacity

Select the bid with highest unit-value, one at a time,while supply and demand lasts

Theorem

The greedy algorithm provides a close-form approximationratio of α and an integrality gap of α to problem PNCone(t)in polynomial time.a

aα = 1 + ε(e − 1) θθ−1

.


Auc2Charge: An Online Auction Framework Properties of Auc2Charge

Properties of Auc2Charge

Theorem

Aucone is computationally efficient, truthful, individual rational,and α(1 + Rmax)-competitive in the one-shot auction ofAuc2Charge online auction framework.a

aRmax : the maximal per-timeslot bid-to-budget ratio.

Theorem

Using Aucone as the one-shot auction, the Auc2Charge frameworkis truthful, individual rational, computationally efficient and(1 + Rmax)(α(1 + Rmax) + 1

ϕ−1)-competitive on the social welfarefor the EV park-and-charge system.a

aϕ = (1 + Rmax)1

Rmax .


Performance Evaluation Simulation Settings

Simulation Settings

Park-and-charge Facility: 500 spots

EV battery capacity: 40kWh

Arriving SOC ∈ (0, 0.7]

Parking time ∈ [2, 6] hours

Budget: ∈ [8, 12] dollars

Number of bids/hour: ≤ 5

Simulated time T = 12, 18, 24 hours

Simulated scale M = 100, 200, 300, 400, 500 EVs


Performance Evaluation Simulation Settings

Simulation Settings

Metrics

Social Welfare

Approximation ratio over offline optimum

User Satisfaction

User Satisfaction Ratio

Unit Charging Payment

Total Charging Payment

Budget Utilization Ratio


Performance Evaluation Evaluation Results

Evaluation Results

Approximation Ratio on Social Welfare

100 200 300 400 5000

0.5

1

1.5

2

2.5

3

Number of Electric Vehicles

Rat

io o

f Offl

ine/

Onl

ine

Soc

ial W

elfa

re

Auc2ChargeOffOptimal

T = 12 Hours

12 18 240

1

2

3

Number of Time SlotsR

atio

of O

fflin

e/O

nlin

e S

ocia

l Wel

fare

Auc2ChargeOffOptimal

M = 100 Electric Vehicles



Evaluation Results

User Satisfaction

100 200 300 400 5000

0.2

0.4

0.6

0.8

1


Ave

rage

of U

ser

Sat

isfa

ctio

n R

atio

T=12T=18T=24

User Satisfaction Ratio

100 200 300 400 5000

0.1

0.2

0.3

0.4

0.5

Number of Electric VehiclesA

vera

ge o

f Uni

t Pay

men

t

T=12T=18T=24

Unit Charging Payment



Evaluation Results

User Satisfaction - Cont’d

100 200 300 400 5000

1

2

3

4


Ave

rage

of T

otal

Pay

men

t

T=12T=18T=24

Total Charging Payment

100 200 300 400 5000

0.1

0.2

0.3

0.4


Ave

rage

of B

udge

t Util

izat

ion

Rat

io

T=12T=18T=24

Budget Utilization Ratio


Concluding Remarks Conclusion and Future Work

Conclusion and Future Work

Conclusion

Explore auctions as efficient market mechanisms for EVcharging stations

Propose Auc2Charge, an online auction framework for EVpark-and-charge

Demonstrate system benefits in terms of social welfareand user satisfaction

Future Work

Include other realistic constraints, e.g., V2G transmissionand ramp-up/down generation cost

Investigate privacy-preserving auctions for EV charging


Documents

Auc2Charge: An Online Auction Framework for Electric ... · Auc2Charge: An Online Auction Framework for Electric Vehicle Park-and-Charge Qiao Xiang1, Fanxin Kong1, Xue Liu1, Xi Chen1,